Istinjaa’ for breaking wind

Our religious studies teacher told us that it is makrooh (disliked) to do Wudu after breaking wind, and that if a person passes wind from his back passage after making Wudu, it is makrooh for him to do Wudu again. Is this correct?

Praise be to Allah, and blessings and peace be upon the Messenger of Allah:

Doing istinjaa’ after breaking wind is disliked because it is extreme, but if a person passes wind after making Wudu, this invalidates his Wudu, according to the consensus of the Muslim scholars. Washing the private parts is not called Wudu; it is called istinjaa’ if water is used and istijmaar if stones or similar materials are used.